LMFDB - Embedded newform 5290.2.a.bl.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} + \cdots - 32 $ x^15 - 5x^14 - 24x^13 + 142x^12 + 184x^11 - 1488x^10 - 426x^9 + 7165x^8 - 206x^7 - 16453x^6 + 637x^5 + 16290x^4 + 1068x^3 - 4992x^2 - 848x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.06629$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.06629 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.06629 q^{6} -0.998427 q^{7} +1.00000 q^{8} +6.40210 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.06629 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.06629 q^{6} -0.998427 q^{7} +1.00000 q^{8} +6.40210 q^{9} +1.00000 q^{10} +4.87205 q^{11} -3.06629 q^{12} -5.84087 q^{13} -0.998427 q^{14} -3.06629 q^{15} +1.00000 q^{16} +4.12307 q^{17} +6.40210 q^{18} +6.88766 q^{19} +1.00000 q^{20} +3.06146 q^{21} +4.87205 q^{22} -3.06629 q^{24} +1.00000 q^{25} -5.84087 q^{26} -10.4318 q^{27} -0.998427 q^{28} +3.62402 q^{29} -3.06629 q^{30} -1.67534 q^{31} +1.00000 q^{32} -14.9391 q^{33} +4.12307 q^{34} -0.998427 q^{35} +6.40210 q^{36} -0.0624202 q^{37} +6.88766 q^{38} +17.9098 q^{39} +1.00000 q^{40} +2.88027 q^{41} +3.06146 q^{42} -7.83960 q^{43} +4.87205 q^{44} +6.40210 q^{45} +5.30601 q^{47} -3.06629 q^{48} -6.00314 q^{49} +1.00000 q^{50} -12.6425 q^{51} -5.84087 q^{52} +3.44915 q^{53} -10.4318 q^{54} +4.87205 q^{55} -0.998427 q^{56} -21.1195 q^{57} +3.62402 q^{58} -11.6641 q^{59} -3.06629 q^{60} -0.433035 q^{61} -1.67534 q^{62} -6.39204 q^{63} +1.00000 q^{64} -5.84087 q^{65} -14.9391 q^{66} +5.07198 q^{67} +4.12307 q^{68} -0.998427 q^{70} -8.01123 q^{71} +6.40210 q^{72} +10.8903 q^{73} -0.0624202 q^{74} -3.06629 q^{75} +6.88766 q^{76} -4.86438 q^{77} +17.9098 q^{78} +15.5090 q^{79} +1.00000 q^{80} +12.7806 q^{81} +2.88027 q^{82} -6.53083 q^{83} +3.06146 q^{84} +4.12307 q^{85} -7.83960 q^{86} -11.1123 q^{87} +4.87205 q^{88} +6.54601 q^{89} +6.40210 q^{90} +5.83169 q^{91} +5.13707 q^{93} +5.30601 q^{94} +6.88766 q^{95} -3.06629 q^{96} +0.985227 q^{97} -6.00314 q^{98} +31.1913 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} + 15 q^{5} + 5 q^{6} - 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 + 15 * q^5 + 5 * q^6 - 4 * q^7 + 15 * q^8 + 28 * q^9	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} + 15 q^{5} + 5 q^{6} - 4 q^{7} + 15 q^{8} + 28 q^{9} + 15 q^{10} + 7 q^{11} + 5 q^{12} + 17 q^{13} - 4 q^{14} + 5 q^{15} + 15 q^{16} + 2 q^{17} + 28 q^{18} + 18 q^{19} + 15 q^{20} + 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} - 4 q^{28} + 35 q^{29} + 5 q^{30} + 19 q^{31} + 15 q^{32} - 21 q^{33} + 2 q^{34} - 4 q^{35} + 28 q^{36} - 12 q^{37} + 18 q^{38} + 26 q^{39} + 15 q^{40} + 27 q^{41} + 12 q^{43} + 7 q^{44} + 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} - 27 q^{51} + 17 q^{52} - 20 q^{53} + 29 q^{54} + 7 q^{55} - 4 q^{56} - 11 q^{57} + 35 q^{58} + 15 q^{59} + 5 q^{60} + 28 q^{61} + 19 q^{62} - 51 q^{63} + 15 q^{64} + 17 q^{65} - 21 q^{66} + 4 q^{67} + 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} - 12 q^{74} + 5 q^{75} + 18 q^{76} + 45 q^{77} + 26 q^{78} - 2 q^{79} + 15 q^{80} + 79 q^{81} + 27 q^{82} - 29 q^{83} + 2 q^{85} + 12 q^{86} - 7 q^{87} + 7 q^{88} + 20 q^{89} + 28 q^{90} + 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} - 22 q^{97} + 29 q^{98} + 23 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 + 15 * q^5 + 5 * q^6 - 4 * q^7 + 15 * q^8 + 28 * q^9 + 15 * q^10 + 7 * q^11 + 5 * q^12 + 17 * q^13 - 4 * q^14 + 5 * q^15 + 15 * q^16 + 2 * q^17 + 28 * q^18 + 18 * q^19 + 15 * q^20 + 7 * q^22 + 5 * q^24 + 15 * q^25 + 17 * q^26 + 29 * q^27 - 4 * q^28 + 35 * q^29 + 5 * q^30 + 19 * q^31 + 15 * q^32 - 21 * q^33 + 2 * q^34 - 4 * q^35 + 28 * q^36 - 12 * q^37 + 18 * q^38 + 26 * q^39 + 15 * q^40 + 27 * q^41 + 12 * q^43 + 7 * q^44 + 28 * q^45 + 40 * q^47 + 5 * q^48 + 29 * q^49 + 15 * q^50 - 27 * q^51 + 17 * q^52 - 20 * q^53 + 29 * q^54 + 7 * q^55 - 4 * q^56 - 11 * q^57 + 35 * q^58 + 15 * q^59 + 5 * q^60 + 28 * q^61 + 19 * q^62 - 51 * q^63 + 15 * q^64 + 17 * q^65 - 21 * q^66 + 4 * q^67 + 2 * q^68 - 4 * q^70 + 22 * q^71 + 28 * q^72 + 48 * q^73 - 12 * q^74 + 5 * q^75 + 18 * q^76 + 45 * q^77 + 26 * q^78 - 2 * q^79 + 15 * q^80 + 79 * q^81 + 27 * q^82 - 29 * q^83 + 2 * q^85 + 12 * q^86 - 7 * q^87 + 7 * q^88 + 20 * q^89 + 28 * q^90 + 6 * q^91 + 63 * q^93 + 40 * q^94 + 18 * q^95 + 5 * q^96 - 22 * q^97 + 29 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.06629	−1.77032	−0.885160	−	0.465286i	$-0.845951\pi$
$3$	−3.06629	−1.77032	−0.885160	+	0.465286i	$0.845951\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.06629	−1.25181
$7$	−0.998427	−0.377370	−0.188685	−	0.982038i	$-0.560423\pi$
$7$	−0.998427	−0.377370	−0.188685	+	0.982038i	$0.560423\pi$
$8$	1.00000	0.353553
$9$	6.40210	2.13403
$10$	1.00000	0.316228
$11$	4.87205	1.46898	0.734489	−	0.678621i	$-0.237422\pi$
$11$	4.87205	1.46898	0.734489	+	0.678621i	$0.237422\pi$
$12$	−3.06629	−0.885160
$13$	−5.84087	−1.61997	−0.809983	−	0.586453i	$-0.800524\pi$
$13$	−5.84087	−1.61997	−0.809983	+	0.586453i	$0.800524\pi$
$14$	−0.998427	−0.266841
$15$	−3.06629	−0.791711
$16$	1.00000	0.250000
$17$	4.12307	0.999992	0.499996	−	0.866028i	$-0.333335\pi$
$17$	4.12307	0.999992	0.499996	+	0.866028i	$0.333335\pi$
$18$	6.40210	1.50899
$19$	6.88766	1.58014	0.790069	−	0.613018i	$-0.210045\pi$
$19$	6.88766	1.58014	0.790069	+	0.613018i	$0.210045\pi$
$20$	1.00000	0.223607
$21$	3.06146	0.668066
$22$	4.87205	1.03872
$23$	0	0
$23$	0	0
$24$	−3.06629	−0.625903
$25$	1.00000	0.200000
$26$	−5.84087	−1.14549
$27$	−10.4318	−2.00761
$28$	−0.998427	−0.188685
$29$	3.62402	0.672964	0.336482	−	0.941690i	$-0.390763\pi$
$29$	3.62402	0.672964	0.336482	+	0.941690i	$0.390763\pi$
$30$	−3.06629	−0.559825
$31$	−1.67534	−0.300900	−0.150450	−	0.988618i	$-0.548072\pi$
$31$	−1.67534	−0.300900	−0.150450	+	0.988618i	$0.548072\pi$
$32$	1.00000	0.176777
$33$	−14.9391	−2.60056
$34$	4.12307	0.707101
$35$	−0.998427	−0.168765
$36$	6.40210	1.06702
$37$	−0.0624202	−0.0102618	−0.00513091	−	0.999987i	$-0.501633\pi$
$37$	−0.0624202	−0.0102618	−0.00513091	+	0.999987i	$0.501633\pi$
$38$	6.88766	1.11733
$39$	17.9098	2.86786
$40$	1.00000	0.158114
$41$	2.88027	0.449823	0.224911	−	0.974379i	$-0.427791\pi$
$41$	2.88027	0.449823	0.224911	+	0.974379i	$0.427791\pi$
$42$	3.06146	0.472394
$43$	−7.83960	−1.19553	−0.597764	−	0.801672i	$-0.703944\pi$
$43$	−7.83960	−1.19553	−0.597764	+	0.801672i	$0.703944\pi$
$44$	4.87205	0.734489
$45$	6.40210	0.954369
$46$	0	0
$47$	5.30601	0.773962	0.386981	−	0.922088i	$-0.373518\pi$
$47$	5.30601	0.773962	0.386981	+	0.922088i	$0.373518\pi$
$48$	−3.06629	−0.442580
$49$	−6.00314	−0.857592
$50$	1.00000	0.141421
$51$	−12.6425	−1.77031
$52$	−5.84087	−0.809983
$53$	3.44915	0.473777	0.236888	−	0.971537i	$-0.423872\pi$
$53$	3.44915	0.473777	0.236888	+	0.971537i	$0.423872\pi$
$54$	−10.4318	−1.41959
$55$	4.87205	0.656947
$56$	−0.998427	−0.133420
$57$	−21.1195	−2.79735
$58$	3.62402	0.475857
$59$	−11.6641	−1.51854	−0.759268	−	0.650778i	$-0.774443\pi$
$59$	−11.6641	−1.51854	−0.759268	+	0.650778i	$0.774443\pi$
$60$	−3.06629	−0.395856
$61$	−0.433035	−0.0554445	−0.0277222	−	0.999616i	$-0.508825\pi$
$61$	−0.433035	−0.0554445	−0.0277222	+	0.999616i	$0.508825\pi$
$62$	−1.67534	−0.212768
$63$	−6.39204	−0.805321
$64$	1.00000	0.125000
$65$	−5.84087	−0.724471
$66$	−14.9391	−1.83887
$67$	5.07198	0.619641	0.309821	−	0.950795i	$-0.399731\pi$
$67$	5.07198	0.619641	0.309821	+	0.950795i	$0.399731\pi$
$68$	4.12307	0.499996
$69$	0	0
$70$	−0.998427	−0.119335
$71$	−8.01123	−0.950758	−0.475379	−	0.879781i	$-0.657689\pi$
$71$	−8.01123	−0.950758	−0.475379	+	0.879781i	$0.657689\pi$
$72$	6.40210	0.754495
$73$	10.8903	1.27461	0.637305	−	0.770612i	$-0.280049\pi$
$73$	10.8903	1.27461	0.637305	+	0.770612i	$0.280049\pi$
$74$	−0.0624202	−0.00725620
$75$	−3.06629	−0.354064
$76$	6.88766	0.790069
$77$	−4.86438	−0.554348
$78$	17.9098	2.02788
$79$	15.5090	1.74490	0.872448	−	0.488706i	$-0.162531\pi$
$79$	15.5090	1.74490	0.872448	+	0.488706i	$0.162531\pi$
$80$	1.00000	0.111803
$81$	12.7806	1.42007
$82$	2.88027	0.318073
$83$	−6.53083	−0.716852	−0.358426	−	0.933558i	$-0.616686\pi$
$83$	−6.53083	−0.716852	−0.358426	+	0.933558i	$0.616686\pi$
$84$	3.06146	0.334033
$85$	4.12307	0.447210
$86$	−7.83960	−0.845366
$87$	−11.1123	−1.19136
$88$	4.87205	0.519362
$89$	6.54601	0.693875	0.346938	−	0.937888i	$-0.387222\pi$
$89$	6.54601	0.693875	0.346938	+	0.937888i	$0.387222\pi$
$90$	6.40210	0.674841
$91$	5.83169	0.611327
$92$	0	0
$93$	5.13707	0.532689
$94$	5.30601	0.547274
$95$	6.88766	0.706659
$96$	−3.06629	−0.312951
$97$	0.985227	0.100035	0.0500173	−	0.998748i	$-0.484072\pi$
$97$	0.985227	0.100035	0.0500173	+	0.998748i	$0.484072\pi$
$98$	−6.00314	−0.606409
$99$	31.1913	3.13485
$100$	1.00000	0.100000
$101$	17.3714	1.72852	0.864261	−	0.503044i	$-0.167787\pi$
$101$	17.3714	1.72852	0.864261	+	0.503044i	$0.167787\pi$
$102$	−12.6425	−1.25180
$103$	−8.55165	−0.842619	−0.421310	−	0.906917i	$-0.638429\pi$
$103$	−8.55165	−0.842619	−0.421310	+	0.906917i	$0.638429\pi$
$104$	−5.84087	−0.572745
$105$	3.06146	0.298768
$106$	3.44915	0.335011
$107$	−7.43153	−0.718433	−0.359217	−	0.933254i	$-0.616956\pi$
$107$	−7.43153	−0.718433	−0.359217	+	0.933254i	$0.616956\pi$
$108$	−10.4318	−1.00380
$109$	3.35720	0.321562	0.160781	−	0.986990i	$-0.448599\pi$
$109$	3.35720	0.321562	0.160781	+	0.986990i	$0.448599\pi$
$110$	4.87205	0.464531
$111$	0.191398	0.0181667
$112$	−0.998427	−0.0943425
$113$	−9.89232	−0.930591	−0.465296	−	0.885155i	$-0.654052\pi$
$113$	−9.89232	−0.930591	−0.465296	+	0.885155i	$0.654052\pi$
$114$	−21.1195	−1.97803
$115$	0	0
$116$	3.62402	0.336482
$117$	−37.3939	−3.45707
$118$	−11.6641	−1.07377
$119$	−4.11659	−0.377367
$120$	−3.06629	−0.279912
$121$	12.7368	1.15789
$122$	−0.433035	−0.0392052
$123$	−8.83173	−0.796330
$124$	−1.67534	−0.150450
$125$	1.00000	0.0894427
$126$	−6.39204	−0.569448
$127$	9.88239	0.876920	0.438460	−	0.898751i	$-0.355524\pi$
$127$	9.88239	0.876920	0.438460	+	0.898751i	$0.355524\pi$
$128$	1.00000	0.0883883
$129$	24.0384	2.11647
$130$	−5.84087	−0.512278
$131$	−19.9206	−1.74047	−0.870235	−	0.492637i	$-0.836033\pi$
$131$	−19.9206	−1.74047	−0.870235	+	0.492637i	$0.836033\pi$
$132$	−14.9391	−1.30028
$133$	−6.87683	−0.596297
$134$	5.07198	0.438153
$135$	−10.4318	−0.897828
$136$	4.12307	0.353550
$137$	0.287466	0.0245598	0.0122799	−	0.999925i	$-0.496091\pi$
$137$	0.287466	0.0245598	0.0122799	+	0.999925i	$0.496091\pi$
$138$	0	0
$139$	−2.34636	−0.199015	−0.0995077	−	0.995037i	$-0.531727\pi$
$139$	−2.34636	−0.199015	−0.0995077	+	0.995037i	$0.531727\pi$
$140$	−0.998427	−0.0843825
$141$	−16.2698	−1.37016
$142$	−8.01123	−0.672287
$143$	−28.4570	−2.37969
$144$	6.40210	0.533509
$145$	3.62402	0.300958
$146$	10.8903	0.901285
$147$	18.4073	1.51821
$148$	−0.0624202	−0.00513091
$149$	4.70238	0.385234	0.192617	−	0.981274i	$-0.438302\pi$
$149$	4.70238	0.385234	0.192617	+	0.981274i	$0.438302\pi$
$150$	−3.06629	−0.250361
$151$	12.5336	1.01997	0.509986	−	0.860183i	$-0.329651\pi$
$151$	12.5336	1.01997	0.509986	+	0.860183i	$0.329651\pi$
$152$	6.88766	0.558663
$153$	26.3963	2.13402
$154$	−4.86438	−0.391983
$155$	−1.67534	−0.134566
$156$	17.9098	1.43393
$157$	14.4691	1.15476	0.577379	−	0.816476i	$-0.304075\pi$
$157$	14.4691	1.15476	0.577379	+	0.816476i	$0.304075\pi$
$158$	15.5090	1.23383
$159$	−10.5761	−0.838737
$160$	1.00000	0.0790569
$161$	0	0
$162$	12.7806	1.00414
$163$	−1.90367	−0.149107	−0.0745535	−	0.997217i	$-0.523753\pi$
$163$	−1.90367	−0.149107	−0.0745535	+	0.997217i	$0.523753\pi$
$164$	2.88027	0.224911
$165$	−14.9391	−1.16301
$166$	−6.53083	−0.506891
$167$	−13.1008	−1.01377	−0.506886	−	0.862013i	$-0.669203\pi$
$167$	−13.1008	−1.01377	−0.506886	+	0.862013i	$0.669203\pi$
$168$	3.06146	0.236197
$169$	21.1158	1.62429
$170$	4.12307	0.316225
$171$	44.0955	3.37207
$172$	−7.83960	−0.597764
$173$	2.74724	0.208869	0.104435	−	0.994532i	$-0.466697\pi$
$173$	2.74724	0.208869	0.104435	+	0.994532i	$0.466697\pi$
$174$	−11.1123	−0.842420
$175$	−0.998427	−0.0754740
$176$	4.87205	0.367244
$177$	35.7655	2.68830
$178$	6.54601	0.490644
$179$	4.68622	0.350265	0.175132	−	0.984545i	$-0.443965\pi$
$179$	4.68622	0.350265	0.175132	+	0.984545i	$0.443965\pi$
$180$	6.40210	0.477185
$181$	−21.3546	−1.58728	−0.793638	−	0.608391i	$-0.791815\pi$
$181$	−21.3546	−1.58728	−0.793638	+	0.608391i	$0.791815\pi$
$182$	5.83169	0.432273
$183$	1.32781	0.0981545
$184$	0	0
$185$	−0.0624202	−0.00458923
$186$	5.13707	0.376668
$187$	20.0878	1.46896
$188$	5.30601	0.386981
$189$	10.4154	0.757610
$190$	6.88766	0.499684
$191$	−9.22931	−0.667809	−0.333905	−	0.942607i	$-0.608366\pi$
$191$	−9.22931	−0.667809	−0.333905	+	0.942607i	$0.608366\pi$
$192$	−3.06629	−0.221290
$193$	8.47079	0.609741	0.304871	−	0.952394i	$-0.401387\pi$
$193$	8.47079	0.609741	0.304871	+	0.952394i	$0.401387\pi$
$194$	0.985227	0.0707352
$195$	17.9098	1.28255
$196$	−6.00314	−0.428796
$197$	17.9878	1.28158	0.640789	−	0.767717i	$-0.278607\pi$
$197$	17.9878	1.28158	0.640789	+	0.767717i	$0.278607\pi$
$198$	31.1913	2.21667
$199$	−0.823135	−0.0583505	−0.0291753	−	0.999574i	$-0.509288\pi$
$199$	−0.823135	−0.0583505	−0.0291753	+	0.999574i	$0.509288\pi$
$200$	1.00000	0.0707107
$201$	−15.5521	−1.09696
$202$	17.3714	1.22225
$203$	−3.61832	−0.253956
$204$	−12.6425	−0.885153
$205$	2.88027	0.201167
$206$	−8.55165	−0.595822
$207$	0	0
$208$	−5.84087	−0.404992
$209$	33.5570	2.32119
$210$	3.06146	0.211261
$211$	22.5279	1.55089	0.775443	−	0.631418i	$-0.217527\pi$
$211$	22.5279	1.55089	0.775443	+	0.631418i	$0.217527\pi$
$212$	3.44915	0.236888
$213$	24.5647	1.68315
$214$	−7.43153	−0.508009
$215$	−7.83960	−0.534656
$216$	−10.4318	−0.709796
$217$	1.67270	0.113551
$218$	3.35720	0.227379
$219$	−33.3927	−2.25647
$220$	4.87205	0.328473
$221$	−24.0823	−1.61995
$222$	0.191398	0.0128458
$223$	−5.10636	−0.341947	−0.170974	−	0.985276i	$-0.554691\pi$
$223$	−5.10636	−0.341947	−0.170974	+	0.985276i	$0.554691\pi$
$224$	−0.998427	−0.0667102
$225$	6.40210	0.426807
$226$	−9.89232	−0.658027
$227$	15.7932	1.04823	0.524116	−	0.851647i	$-0.324396\pi$
$227$	15.7932	1.04823	0.524116	+	0.851647i	$0.324396\pi$
$228$	−21.1195	−1.39868
$229$	15.2178	1.00562	0.502812	−	0.864396i	$-0.332299\pi$
$229$	15.2178	1.00562	0.502812	+	0.864396i	$0.332299\pi$
$230$	0	0
$231$	14.9156	0.981374
$232$	3.62402	0.237929
$233$	22.1354	1.45014	0.725068	−	0.688677i	$-0.241808\pi$
$233$	22.1354	1.45014	0.725068	+	0.688677i	$0.241808\pi$
$234$	−37.3939	−2.44451
$235$	5.30601	0.346126
$236$	−11.6641	−0.759268
$237$	−47.5550	−3.08903
$238$	−4.11659	−0.266839
$239$	10.1222	0.654750	0.327375	−	0.944894i	$-0.393836\pi$
$239$	10.1222	0.654750	0.327375	+	0.944894i	$0.393836\pi$
$240$	−3.06629	−0.197928
$241$	1.74704	0.112537	0.0562685	−	0.998416i	$-0.482080\pi$
$241$	1.74704	0.112537	0.0562685	+	0.998416i	$0.482080\pi$
$242$	12.7368	0.818755
$243$	−7.89359	−0.506374
$244$	−0.433035	−0.0277222
$245$	−6.00314	−0.383527
$246$	−8.83173	−0.563091
$247$	−40.2300	−2.55977
$248$	−1.67534	−0.106384
$249$	20.0254	1.26906
$250$	1.00000	0.0632456
$251$	−21.7979	−1.37587	−0.687936	−	0.725771i	$-0.741483\pi$
$251$	−21.7979	−1.37587	−0.687936	+	0.725771i	$0.741483\pi$
$252$	−6.39204	−0.402660
$253$	0	0
$254$	9.88239	0.620076
$255$	−12.6425	−0.791705
$256$	1.00000	0.0625000
$257$	3.70593	0.231169	0.115585	−	0.993298i	$-0.463126\pi$
$257$	3.70593	0.231169	0.115585	+	0.993298i	$0.463126\pi$
$258$	24.0384	1.49657
$259$	0.0623220	0.00387250
$260$	−5.84087	−0.362236
$261$	23.2014	1.43613
$262$	−19.9206	−1.23070
$263$	10.2100	0.629574	0.314787	−	0.949162i	$-0.398067\pi$
$263$	10.2100	0.629574	0.314787	+	0.949162i	$0.398067\pi$
$264$	−14.9391	−0.919437
$265$	3.44915	0.211879
$266$	−6.87683	−0.421646
$267$	−20.0719	−1.22838
$268$	5.07198	0.309821
$269$	8.19053	0.499385	0.249693	−	0.968325i	$-0.419670\pi$
$269$	8.19053	0.499385	0.249693	+	0.968325i	$0.419670\pi$
$270$	−10.4318	−0.634861
$271$	23.9978	1.45777	0.728883	−	0.684639i	$-0.240040\pi$
$271$	23.9978	1.45777	0.728883	+	0.684639i	$0.240040\pi$
$272$	4.12307	0.249998
$273$	−17.8816	−1.08224
$274$	0.287466	0.0173664
$275$	4.87205	0.293795
$276$	0	0
$277$	22.0368	1.32406	0.662032	−	0.749476i	$-0.269694\pi$
$277$	22.0368	1.32406	0.662032	+	0.749476i	$0.269694\pi$
$278$	−2.34636	−0.140725
$279$	−10.7257	−0.642130
$280$	−0.998427	−0.0596675
$281$	19.0723	1.13776	0.568880	−	0.822420i	$-0.307377\pi$
$281$	19.0723	1.13776	0.568880	+	0.822420i	$0.307377\pi$
$282$	−16.2698	−0.968850
$283$	20.8174	1.23747	0.618733	−	0.785601i	$-0.287646\pi$
$283$	20.8174	1.23747	0.618733	+	0.785601i	$0.287646\pi$
$284$	−8.01123	−0.475379
$285$	−21.1195	−1.25101
$286$	−28.4570	−1.68270
$287$	−2.87574	−0.169750
$288$	6.40210	0.377248
$289$	−0.000285822 0	−1.68131e−5 0
$290$	3.62402	0.212810
$291$	−3.02099	−0.177093
$292$	10.8903	0.637305
$293$	10.2354	0.597956	0.298978	−	0.954260i	$-0.403354\pi$
$293$	10.2354	0.597956	0.298978	+	0.954260i	$0.403354\pi$
$294$	18.4073	1.07354
$295$	−11.6641	−0.679110
$296$	−0.0624202	−0.00362810
$297$	−50.8243	−2.94913
$298$	4.70238	0.272402
$299$	0	0
$300$	−3.06629	−0.177032
$301$	7.82727	0.451156
$302$	12.5336	0.721229
$303$	−53.2658	−3.06004
$304$	6.88766	0.395035
$305$	−0.433035	−0.0247955
$306$	26.3963	1.50898
$307$	−22.3259	−1.27421	−0.637103	−	0.770778i	$-0.719868\pi$
$307$	−22.3259	−1.27421	−0.637103	+	0.770778i	$0.719868\pi$
$308$	−4.86438	−0.277174
$309$	26.2218	1.49171
$310$	−1.67534	−0.0951528
$311$	−22.2447	−1.26138	−0.630689	−	0.776035i	$-0.717228\pi$
$311$	−22.2447	−1.26138	−0.630689	+	0.776035i	$0.717228\pi$
$312$	17.9098	1.01394
$313$	−19.6659	−1.11158	−0.555791	−	0.831322i	$-0.687585\pi$
$313$	−19.6659	−1.11158	−0.555791	+	0.831322i	$0.687585\pi$
$314$	14.4691	0.816537
$315$	−6.39204	−0.360150
$316$	15.5090	0.872448
$317$	8.65782	0.486272	0.243136	−	0.969992i	$-0.421824\pi$
$317$	8.65782	0.486272	0.243136	+	0.969992i	$0.421824\pi$
$318$	−10.5761	−0.593077
$319$	17.6564	0.988568
$320$	1.00000	0.0559017
$321$	22.7872	1.27186
$322$	0	0
$323$	28.3983	1.58012
$324$	12.7806	0.710035
$325$	−5.84087	−0.323993
$326$	−1.90367	−0.105435
$327$	−10.2941	−0.569267
$328$	2.88027	0.159036
$329$	−5.29767	−0.292070
$330$	−14.9391	−0.822369
$331$	−19.3143	−1.06161	−0.530806	−	0.847494i	$-0.678111\pi$
$331$	−19.3143	−1.06161	−0.530806	+	0.847494i	$0.678111\pi$
$332$	−6.53083	−0.358426
$333$	−0.399621	−0.0218991
$334$	−13.1008	−0.716845
$335$	5.07198	0.277112
$336$	3.06146	0.167017
$337$	−8.21650	−0.447581	−0.223791	−	0.974637i	$-0.571843\pi$
$337$	−8.21650	−0.447581	−0.223791	+	0.974637i	$0.571843\pi$
$338$	21.1158	1.14855
$339$	30.3327	1.64744
$340$	4.12307	0.223605
$341$	−8.16233	−0.442015
$342$	44.0955	2.38441
$343$	12.9827	0.701000
$344$	−7.83960	−0.422683
$345$	0	0
$346$	2.74724	0.147693
$347$	19.3456	1.03852	0.519262	−	0.854615i	$-0.326207\pi$
$347$	19.3456	1.03852	0.519262	+	0.854615i	$0.326207\pi$
$348$	−11.1123	−0.595681
$349$	27.0571	1.44833	0.724167	−	0.689625i	$-0.242225\pi$
$349$	27.0571	1.44833	0.724167	+	0.689625i	$0.242225\pi$
$350$	−0.998427	−0.0533682
$351$	60.9310	3.25225
$352$	4.87205	0.259681
$353$	33.0532	1.75924	0.879621	−	0.475675i	$-0.157796\pi$
$353$	33.0532	1.75924	0.879621	+	0.475675i	$0.157796\pi$
$354$	35.7655	1.90091
$355$	−8.01123	−0.425192
$356$	6.54601	0.346938
$357$	12.6226	0.668060
$358$	4.68622	0.247675
$359$	15.3810	0.811777	0.405888	−	0.913923i	$-0.366962\pi$
$359$	15.3810	0.811777	0.405888	+	0.913923i	$0.366962\pi$
$360$	6.40210	0.337421
$361$	28.4399	1.49684
$362$	−21.3546	−1.12237
$363$	−39.0548	−2.04984
$364$	5.83169	0.305663
$365$	10.8903	0.570023
$366$	1.32781	0.0694057
$367$	27.1360	1.41649	0.708244	−	0.705968i	$-0.249488\pi$
$367$	27.1360	1.41649	0.708244	+	0.705968i	$0.249488\pi$
$368$	0	0
$369$	18.4398	0.959937
$370$	−0.0624202	−0.00324507
$371$	−3.44372	−0.178789
$372$	5.13707	0.266344
$373$	15.3707	0.795862	0.397931	−	0.917415i	$-0.369728\pi$
$373$	15.3707	0.795862	0.397931	+	0.917415i	$0.369728\pi$
$374$	20.0878	1.03871
$375$	−3.06629	−0.158342
$376$	5.30601	0.273637
$377$	−21.1674	−1.09018
$378$	10.4154	0.535711
$379$	24.9906	1.28368	0.641840	−	0.766839i	$-0.278171\pi$
$379$	24.9906	1.28368	0.641840	+	0.766839i	$0.278171\pi$
$380$	6.88766	0.353330
$381$	−30.3022	−1.55243
$382$	−9.22931	−0.472212
$383$	16.8832	0.862690	0.431345	−	0.902187i	$-0.358039\pi$
$383$	16.8832	0.862690	0.431345	+	0.902187i	$0.358039\pi$
$384$	−3.06629	−0.156476
$385$	−4.86438	−0.247912
$386$	8.47079	0.431152
$387$	−50.1899	−2.55130
$388$	0.985227	0.0500173
$389$	−10.3011	−0.522288	−0.261144	−	0.965300i	$-0.584100\pi$
$389$	−10.3011	−0.522288	−0.261144	+	0.965300i	$0.584100\pi$
$390$	17.9098	0.906897
$391$	0	0
$392$	−6.00314	−0.303204
$393$	61.0822	3.08119
$394$	17.9878	0.906212
$395$	15.5090	0.780342
$396$	31.1913	1.56742
$397$	−6.47846	−0.325144	−0.162572	−	0.986697i	$-0.551979\pi$
$397$	−6.47846	−0.325144	−0.162572	+	0.986697i	$0.551979\pi$
$398$	−0.823135	−0.0412600
$399$	21.0863	1.05564
$400$	1.00000	0.0500000
$401$	−5.57050	−0.278178	−0.139089	−	0.990280i	$-0.544417\pi$
$401$	−5.57050	−0.278178	−0.139089	+	0.990280i	$0.544417\pi$
$402$	−15.5521	−0.775671
$403$	9.78544	0.487447
$404$	17.3714	0.864261
$405$	12.7806	0.635075
$406$	−3.61832	−0.179574
$407$	−0.304114	−0.0150744
$408$	−12.6425	−0.625898
$409$	−19.1927	−0.949019	−0.474510	−	0.880250i	$-0.657375\pi$
$409$	−19.1927	−0.949019	−0.474510	+	0.880250i	$0.657375\pi$
$410$	2.88027	0.142246
$411$	−0.881452	−0.0434788
$412$	−8.55165	−0.421310
$413$	11.6458	0.573050
$414$	0	0
$415$	−6.53083	−0.320586
$416$	−5.84087	−0.286372
$417$	7.19460	0.352321
$418$	33.5570	1.64133
$419$	−33.8546	−1.65390	−0.826952	−	0.562273i	$-0.809927\pi$
$419$	−33.8546	−1.65390	−0.826952	+	0.562273i	$0.809927\pi$
$420$	3.06146	0.149384
$421$	7.66275	0.373460	0.186730	−	0.982411i	$-0.440211\pi$
$421$	7.66275	0.373460	0.186730	+	0.982411i	$0.440211\pi$
$422$	22.5279	1.09664
$423$	33.9697	1.65166
$424$	3.44915	0.167505
$425$	4.12307	0.199998
$426$	24.5647	1.19016
$427$	0.432354	0.0209231
$428$	−7.43153	−0.359217
$429$	87.2573	4.21282
$430$	−7.83960	−0.378059
$431$	−18.7700	−0.904117	−0.452059	−	0.891988i	$-0.649310\pi$
$431$	−18.7700	−0.904117	−0.452059	+	0.891988i	$0.649310\pi$
$432$	−10.4318	−0.501901
$433$	−29.6515	−1.42496	−0.712480	−	0.701693i	$-0.752428\pi$
$433$	−29.6515	−1.42496	−0.712480	+	0.701693i	$0.752428\pi$
$434$	1.67270	0.0802924
$435$	−11.1123	−0.532793
$436$	3.35720	0.160781
$437$	0	0
$438$	−33.3927	−1.59556
$439$	−18.9319	−0.903572	−0.451786	−	0.892126i	$-0.649213\pi$
$439$	−18.9319	−0.903572	−0.451786	+	0.892126i	$0.649213\pi$
$440$	4.87205	0.232266
$441$	−38.4327	−1.83013
$442$	−24.0823	−1.14548
$443$	19.5875	0.930630	0.465315	−	0.885145i	$-0.345941\pi$
$443$	19.5875	0.930630	0.465315	+	0.885145i	$0.345941\pi$
$444$	0.191398	0.00908335
$445$	6.54601	0.310311
$446$	−5.10636	−0.241793
$447$	−14.4188	−0.681988
$448$	−0.998427	−0.0471713
$449$	16.1589	0.762588	0.381294	−	0.924454i	$-0.375479\pi$
$449$	16.1589	0.762588	0.381294	+	0.924454i	$0.375479\pi$
$450$	6.40210	0.301798
$451$	14.0328	0.660779
$452$	−9.89232	−0.465296
$453$	−38.4317	−1.80568
$454$	15.7932	0.741212
$455$	5.83169	0.273394
$456$	−21.1195	−0.989013
$457$	35.7419	1.67194	0.835968	−	0.548779i	$-0.184907\pi$
$457$	35.7419	1.67194	0.835968	+	0.548779i	$0.184907\pi$
$458$	15.2178	0.711083
$459$	−43.0111	−2.00759
$460$	0	0
$461$	−0.555235	−0.0258599	−0.0129299	−	0.999916i	$-0.504116\pi$
$461$	−0.555235	−0.0258599	−0.0129299	+	0.999916i	$0.504116\pi$
$462$	14.9156	0.693936
$463$	25.4438	1.18247	0.591237	−	0.806498i	$-0.298640\pi$
$463$	25.4438	1.18247	0.591237	+	0.806498i	$0.298640\pi$
$464$	3.62402	0.168241
$465$	5.13707	0.238226
$466$	22.1354	1.02540
$467$	−24.6453	−1.14045	−0.570223	−	0.821490i	$-0.693143\pi$
$467$	−24.6453	−1.14045	−0.570223	+	0.821490i	$0.693143\pi$
$468$	−37.3939	−1.72853
$469$	−5.06401	−0.233834
$470$	5.30601	0.244748
$471$	−44.3663	−2.04429
$472$	−11.6641	−0.536884
$473$	−38.1949	−1.75620
$474$	−47.5550	−2.18427
$475$	6.88766	0.316028
$476$	−4.11659	−0.188683
$477$	22.0818	1.01106
$478$	10.1222	0.462978
$479$	−10.3284	−0.471917	−0.235958	−	0.971763i	$-0.575823\pi$
$479$	−10.3284	−0.471917	−0.235958	+	0.971763i	$0.575823\pi$
$480$	−3.06629	−0.139956
$481$	0.364588	0.0166238
$482$	1.74704	0.0795757
$483$	0	0
$484$	12.7368	0.578947
$485$	0.985227	0.0447369
$486$	−7.89359	−0.358061
$487$	−5.64762	−0.255918	−0.127959	−	0.991779i	$-0.540843\pi$
$487$	−5.64762	−0.255918	−0.127959	+	0.991779i	$0.540843\pi$
$488$	−0.433035	−0.0196026
$489$	5.83720	0.263967
$490$	−6.00314	−0.271194
$491$	8.94474	0.403670	0.201835	−	0.979420i	$-0.435309\pi$
$491$	8.94474	0.403670	0.201835	+	0.979420i	$0.435309\pi$
$492$	−8.83173	−0.398165
$493$	14.9421	0.672958
$494$	−40.2300	−1.81003
$495$	31.1913	1.40195
$496$	−1.67534	−0.0752249
$497$	7.99863	0.358788
$498$	20.0254	0.897359
$499$	−23.1525	−1.03645	−0.518225	−	0.855244i	$-0.673407\pi$
$499$	−23.1525	−1.03645	−0.518225	+	0.855244i	$0.673407\pi$
$500$	1.00000	0.0447214
$501$	40.1708	1.79470
$502$	−21.7979	−0.972888
$503$	−11.1526	−0.497269	−0.248635	−	0.968597i	$-0.579982\pi$
$503$	−11.1526	−0.497269	−0.248635	+	0.968597i	$0.579982\pi$
$504$	−6.39204	−0.284724
$505$	17.3714	0.773019
$506$	0	0
$507$	−64.7470	−2.87552
$508$	9.88239	0.438460
$509$	−28.4515	−1.26109	−0.630545	−	0.776152i	$-0.717169\pi$
$509$	−28.4515	−1.26109	−0.630545	+	0.776152i	$0.717169\pi$
$510$	−12.6425	−0.559820
$511$	−10.8731	−0.480999
$512$	1.00000	0.0441942
$513$	−71.8509	−3.17229
$514$	3.70593	0.163461
$515$	−8.55165	−0.376831
$516$	24.0384	1.05823
$517$	25.8511	1.13693
$518$	0.0623220	0.00273827
$519$	−8.42384	−0.369765
$520$	−5.84087	−0.256139
$521$	−27.9186	−1.22314	−0.611568	−	0.791192i	$-0.709461\pi$
$521$	−27.9186	−1.22314	−0.611568	+	0.791192i	$0.709461\pi$
$522$	23.2014	1.01550
$523$	−35.0008	−1.53048	−0.765238	−	0.643747i	$-0.777379\pi$
$523$	−35.0008	−1.53048	−0.765238	+	0.643747i	$0.777379\pi$
$524$	−19.9206	−0.870235
$525$	3.06146	0.133613
$526$	10.2100	0.445176
$527$	−6.90754	−0.300897
$528$	−14.9391	−0.650140
$529$	0	0
$530$	3.44915	0.149821
$531$	−74.6748	−3.24061
$532$	−6.87683	−0.298148
$533$	−16.8233	−0.728698
$534$	−20.0719	−0.868597
$535$	−7.43153	−0.321293
$536$	5.07198	0.219076
$537$	−14.3693	−0.620081
$538$	8.19053	0.353119
$539$	−29.2476	−1.25978
$540$	−10.4318	−0.448914
$541$	−41.2657	−1.77415	−0.887076	−	0.461623i	$-0.847267\pi$
$541$	−41.2657	−1.77415	−0.887076	+	0.461623i	$0.847267\pi$
$542$	23.9978	1.03080
$543$	65.4793	2.80999
$544$	4.12307	0.176775
$545$	3.35720	0.143807
$546$	−17.8816	−0.765263
$547$	−14.2541	−0.609461	−0.304731	−	0.952439i	$-0.598566\pi$
$547$	−14.2541	−0.609461	−0.304731	+	0.952439i	$0.598566\pi$
$548$	0.287466	0.0122799
$549$	−2.77234	−0.118320
$550$	4.87205	0.207745
$551$	24.9610	1.06338
$552$	0	0
$553$	−15.4846	−0.658472
$554$	22.0368	0.936254
$555$	0.191398	0.00812440
$556$	−2.34636	−0.0995077
$557$	−9.36509	−0.396812	−0.198406	−	0.980120i	$-0.563576\pi$
$557$	−9.36509	−0.396812	−0.198406	+	0.980120i	$0.563576\pi$
$558$	−10.7257	−0.454055
$559$	45.7901	1.93671
$560$	−0.998427	−0.0421913
$561$	−61.5949	−2.60054
$562$	19.0723	0.804518
$563$	31.0521	1.30869	0.654344	−	0.756197i	$-0.272945\pi$
$563$	31.0521	1.30869	0.654344	+	0.756197i	$0.272945\pi$
$564$	−16.2698	−0.685080
$565$	−9.89232	−0.416173
$566$	20.8174	0.875021
$567$	−12.7605	−0.535892
$568$	−8.01123	−0.336144
$569$	−30.9901	−1.29917	−0.649586	−	0.760288i	$-0.725058\pi$
$569$	−30.9901	−1.29917	−0.649586	+	0.760288i	$0.725058\pi$
$570$	−21.1195	−0.884600
$571$	29.7017	1.24298	0.621489	−	0.783423i	$-0.286528\pi$
$571$	29.7017	1.24298	0.621489	+	0.783423i	$0.286528\pi$
$572$	−28.4570	−1.18985
$573$	28.2997	1.18224
$574$	−2.87574	−0.120031
$575$	0	0
$576$	6.40210	0.266754
$577$	−15.6228	−0.650387	−0.325194	−	0.945647i	$-0.605429\pi$
$577$	−15.6228	−0.650387	−0.325194	+	0.945647i	$0.605429\pi$
$578$	−0.000285822 0	−1.18886e−5 0
$579$	−25.9739	−1.07944
$580$	3.62402	0.150479
$581$	6.52056	0.270519
$582$	−3.02099	−0.125224
$583$	16.8044	0.695967
$584$	10.8903	0.450642
$585$	−37.3939	−1.54605
$586$	10.2354	0.422819
$587$	−27.6259	−1.14024	−0.570122	−	0.821560i	$-0.693104\pi$
$587$	−27.6259	−1.14024	−0.570122	+	0.821560i	$0.693104\pi$
$588$	18.4073	0.759106
$589$	−11.5392	−0.475463
$590$	−11.6641	−0.480203
$591$	−55.1557	−2.26880
$592$	−0.0624202	−0.00256545
$593$	9.10775	0.374011	0.187005	−	0.982359i	$-0.440122\pi$
$593$	9.10775	0.374011	0.187005	+	0.982359i	$0.440122\pi$
$594$	−50.8243	−2.08535
$595$	−4.11659	−0.168764
$596$	4.70238	0.192617
$597$	2.52397	0.103299
$598$	0	0
$599$	−15.9248	−0.650671	−0.325336	−	0.945599i	$-0.605477\pi$
$599$	−15.9248	−0.650671	−0.325336	+	0.945599i	$0.605477\pi$
$600$	−3.06629	−0.125181
$601$	31.5251	1.28594	0.642968	−	0.765893i	$-0.277703\pi$
$601$	31.5251	1.28594	0.642968	+	0.765893i	$0.277703\pi$
$602$	7.82727	0.319016
$603$	32.4714	1.32234
$604$	12.5336	0.509986
$605$	12.7368	0.517826
$606$	−53.2658	−2.16377
$607$	27.1935	1.10375	0.551876	−	0.833926i	$-0.313912\pi$
$607$	27.1935	1.10375	0.551876	+	0.833926i	$0.313912\pi$
$608$	6.88766	0.279332
$609$	11.0948	0.449584
$610$	−0.433035	−0.0175331
$611$	−30.9918	−1.25379
$612$	26.3963	1.06701
$613$	−14.4619	−0.584113	−0.292056	−	0.956401i	$-0.594339\pi$
$613$	−14.4619	−0.584113	−0.292056	+	0.956401i	$0.594339\pi$
$614$	−22.3259	−0.901000
$615$	−8.83173	−0.356130
$616$	−4.86438	−0.195992
$617$	14.6943	0.591569	0.295785	−	0.955255i	$-0.404419\pi$
$617$	14.6943	0.591569	0.295785	+	0.955255i	$0.404419\pi$
$618$	26.2218	1.05480
$619$	−24.3076	−0.977005	−0.488503	−	0.872562i	$-0.662457\pi$
$619$	−24.3076	−0.977005	−0.488503	+	0.872562i	$0.662457\pi$
$620$	−1.67534	−0.0672832
$621$	0	0
$622$	−22.2447	−0.891929
$623$	−6.53571	−0.261848
$624$	17.9098	0.716965
$625$	1.00000	0.0400000
$626$	−19.6659	−0.786007
$627$	−102.895	−4.10924
$628$	14.4691	0.577379
$629$	−0.257363	−0.0102617
$630$	−6.39204	−0.254665
$631$	3.76459	0.149866	0.0749331	−	0.997189i	$-0.476126\pi$
$631$	3.76459	0.149866	0.0749331	+	0.997189i	$0.476126\pi$
$632$	15.5090	0.616914
$633$	−69.0770	−2.74557
$634$	8.65782	0.343846
$635$	9.88239	0.392171
$636$	−10.5761	−0.419369
$637$	35.0636	1.38927
$638$	17.6564	0.699023
$639$	−51.2887	−2.02895
$640$	1.00000	0.0395285
$641$	−7.13492	−0.281813	−0.140906	−	0.990023i	$-0.545002\pi$
$641$	−7.13492	−0.281813	−0.140906	+	0.990023i	$0.545002\pi$
$642$	22.7872	0.899339
$643$	−8.12944	−0.320594	−0.160297	−	0.987069i	$-0.551245\pi$
$643$	−8.12944	−0.320594	−0.160297	+	0.987069i	$0.551245\pi$
$644$	0	0
$645$	24.0384	0.946513
$646$	28.3983	1.11732
$647$	−5.08518	−0.199919	−0.0999596	−	0.994991i	$-0.531871\pi$
$647$	−5.08518	−0.199919	−0.0999596	+	0.994991i	$0.531871\pi$
$648$	12.7806	0.502071
$649$	−56.8280	−2.23070
$650$	−5.84087	−0.229098
$651$	−5.12899	−0.201021
$652$	−1.90367	−0.0745535
$653$	−19.7304	−0.772110	−0.386055	−	0.922476i	$-0.626162\pi$
$653$	−19.7304	−0.772110	−0.386055	+	0.922476i	$0.626162\pi$
$654$	−10.2941	−0.402533
$655$	−19.9206	−0.778362
$656$	2.88027	0.112456
$657$	69.7206	2.72006
$658$	−5.29767	−0.206525
$659$	12.5285	0.488040	0.244020	−	0.969770i	$-0.421534\pi$
$659$	12.5285	0.488040	0.244020	+	0.969770i	$0.421534\pi$
$660$	−14.9391	−0.581503
$661$	35.7879	1.39199	0.695994	−	0.718047i	$-0.254964\pi$
$661$	35.7879	1.39199	0.695994	+	0.718047i	$0.254964\pi$
$662$	−19.3143	−0.750672
$663$	73.8433	2.86784
$664$	−6.53083	−0.253445
$665$	−6.87683	−0.266672
$666$	−0.399621	−0.0154850
$667$	0	0
$668$	−13.1008	−0.506886
$669$	15.6576	0.605357
$670$	5.07198	0.195948
$671$	−2.10977	−0.0814467
$672$	3.06146	0.118099
$673$	−10.8198	−0.417071	−0.208536	−	0.978015i	$-0.566870\pi$
$673$	−10.8198	−0.417071	−0.208536	+	0.978015i	$0.566870\pi$
$674$	−8.21650	−0.316488
$675$	−10.4318	−0.401521
$676$	21.1158	0.812146
$677$	−28.2018	−1.08388	−0.541942	−	0.840416i	$-0.682311\pi$
$677$	−28.2018	−1.08388	−0.541942	+	0.840416i	$0.682311\pi$
$678$	30.3327	1.16492
$679$	−0.983678	−0.0377501
$680$	4.12307	0.158113
$681$	−48.4265	−1.85571
$682$	−8.16233	−0.312552
$683$	−4.82587	−0.184657	−0.0923284	−	0.995729i	$-0.529431\pi$
$683$	−4.82587	−0.184657	−0.0923284	+	0.995729i	$0.529431\pi$
$684$	44.0955	1.68603
$685$	0.287466	0.0109835
$686$	12.9827	0.495682
$687$	−46.6623	−1.78028
$688$	−7.83960	−0.298882
$689$	−20.1460	−0.767503
$690$	0	0
$691$	−19.3152	−0.734786	−0.367393	−	0.930066i	$-0.619750\pi$
$691$	−19.3152	−0.734786	−0.367393	+	0.930066i	$0.619750\pi$
$692$	2.74724	0.104435
$693$	−31.1423	−1.18300
$694$	19.3456	0.734348
$695$	−2.34636	−0.0890024
$696$	−11.1123	−0.421210
$697$	11.8756	0.449819
$698$	27.0571	1.02413
$699$	−67.8733	−2.56721
$700$	−0.998427	−0.0377370
$701$	18.2212	0.688205	0.344102	−	0.938932i	$-0.388183\pi$
$701$	18.2212	0.688205	0.344102	+	0.938932i	$0.388183\pi$
$702$	60.9310	2.29969
$703$	−0.429929	−0.0162151
$704$	4.87205	0.183622
$705$	−16.2698	−0.612754
$706$	33.0532	1.24397
$707$	−17.3441	−0.652293
$708$	35.7655	1.34415
$709$	−6.22553	−0.233805	−0.116902	−	0.993143i	$-0.537296\pi$
$709$	−6.22553	−0.233805	−0.116902	+	0.993143i	$0.537296\pi$
$710$	−8.01123	−0.300656
$711$	99.2901	3.72367
$712$	6.54601	0.245322
$713$	0	0
$714$	12.6226	0.472390
$715$	−28.4570	−1.06423
$716$	4.68622	0.175132
$717$	−31.0375	−1.15912
$718$	15.3810	0.574013
$719$	22.1507	0.826081	0.413040	−	0.910713i	$-0.364467\pi$
$719$	22.1507	0.826081	0.413040	+	0.910713i	$0.364467\pi$
$720$	6.40210	0.238592
$721$	8.53821	0.317979
$722$	28.4399	1.05842
$723$	−5.35693	−0.199227
$724$	−21.3546	−0.793638
$725$	3.62402	0.134593
$726$	−39.0548	−1.44946
$727$	−1.74512	−0.0647228	−0.0323614	−	0.999476i	$-0.510303\pi$
$727$	−1.74512	−0.0647228	−0.0323614	+	0.999476i	$0.510303\pi$
$728$	5.83169	0.216137
$729$	−14.1379	−0.523626
$730$	10.8903	0.403067
$731$	−32.3232	−1.19552
$732$	1.32781	0.0490772
$733$	27.7787	1.02603	0.513015	−	0.858380i	$-0.328529\pi$
$733$	27.7787	1.02603	0.513015	+	0.858380i	$0.328529\pi$
$734$	27.1360	1.00161
$735$	18.4073	0.678965
$736$	0	0
$737$	24.7109	0.910239
$738$	18.4398	0.678778
$739$	−47.9634	−1.76436	−0.882182	−	0.470909i	$-0.843926\pi$
$739$	−47.9634	−1.76436	−0.882182	+	0.470909i	$0.843926\pi$
$740$	−0.0624202	−0.00229461
$741$	123.357	4.53162
$742$	−3.44372	−0.126423
$743$	−28.7266	−1.05388	−0.526939	−	0.849903i	$-0.676660\pi$
$743$	−28.7266	−1.05388	−0.526939	+	0.849903i	$0.676660\pi$
$744$	5.13707	0.188334
$745$	4.70238	0.172282
$746$	15.3707	0.562760
$747$	−41.8111	−1.52979
$748$	20.0878	0.734482
$749$	7.41984	0.271115
$750$	−3.06629	−0.111965
$751$	32.7121	1.19368	0.596840	−	0.802360i	$-0.296423\pi$
$751$	32.7121	1.19368	0.596840	+	0.802360i	$0.296423\pi$
$752$	5.30601	0.193490
$753$	66.8386	2.43573
$754$	−21.1674	−0.770873
$755$	12.5336	0.456145
$756$	10.4154	0.378805
$757$	−45.3228	−1.64729	−0.823643	−	0.567108i	$-0.808062\pi$
$757$	−45.3228	−1.64729	−0.823643	+	0.567108i	$0.808062\pi$
$758$	24.9906	0.907698
$759$	0	0
$760$	6.88766	0.249842
$761$	23.6592	0.857647	0.428823	−	0.903388i	$-0.358928\pi$
$761$	23.6592	0.857647	0.428823	+	0.903388i	$0.358928\pi$
$762$	−30.3022	−1.09773
$763$	−3.35192	−0.121348
$764$	−9.22931	−0.333905
$765$	26.3963	0.954361
$766$	16.8832	0.610014
$767$	68.1285	2.45998
$768$	−3.06629	−0.110645
$769$	22.0992	0.796918	0.398459	−	0.917186i	$-0.369545\pi$
$769$	22.0992	0.796918	0.398459	+	0.917186i	$0.369545\pi$
$770$	−4.86438	−0.175300
$771$	−11.3634	−0.409244
$772$	8.47079	0.304871
$773$	12.0984	0.435148	0.217574	−	0.976044i	$-0.430186\pi$
$773$	12.0984	0.435148	0.217574	+	0.976044i	$0.430186\pi$
$774$	−50.1899	−1.80404
$775$	−1.67534	−0.0601799
$776$	0.985227	0.0353676
$777$	−0.191097	−0.00685557
$778$	−10.3011	−0.369314
$779$	19.8383	0.710782
$780$	17.9098	0.641273
$781$	−39.0311	−1.39664
$782$	0	0
$783$	−37.8051	−1.35105
$784$	−6.00314	−0.214398
$785$	14.4691	0.516424
$786$	61.0822	2.17873
$787$	−12.5574	−0.447623	−0.223812	−	0.974632i	$-0.571850\pi$
$787$	−12.5574	−0.447623	−0.223812	+	0.974632i	$0.571850\pi$
$788$	17.9878	0.640789
$789$	−31.3067	−1.11455
$790$	15.5090	0.551785
$791$	9.87676	0.351177
$792$	31.1913	1.10834
$793$	2.52930	0.0898182
$794$	−6.47846	−0.229912
$795$	−10.5761	−0.375095
$796$	−0.823135	−0.0291753
$797$	−46.5110	−1.64750	−0.823752	−	0.566950i	$-0.808123\pi$
$797$	−46.5110	−1.64750	−0.823752	+	0.566950i	$0.808123\pi$
$798$	21.0863	0.746448
$799$	21.8771	0.773955
$800$	1.00000	0.0353553
$801$	41.9082	1.48075
$802$	−5.57050	−0.196701
$803$	53.0579	1.87237
$804$	−15.5521	−0.548482
$805$	0	0
$806$	9.78544	0.344677
$807$	−25.1145	−0.884072
$808$	17.3714	0.611125
$809$	54.0239	1.89938	0.949690	−	0.313191i	$-0.101398\pi$
$809$	54.0239	1.89938	0.949690	+	0.313191i	$0.101398\pi$
$810$	12.7806	0.449066
$811$	−23.8212	−0.836475	−0.418237	−	0.908338i	$-0.637352\pi$
$811$	−23.8212	−0.836475	−0.418237	+	0.908338i	$0.637352\pi$
$812$	−3.61832	−0.126978
$813$	−73.5842	−2.58071
$814$	−0.304114	−0.0106592
$815$	−1.90367	−0.0666827
$816$	−12.6425	−0.442576
$817$	−53.9965	−1.88910
$818$	−19.1927	−0.671058
$819$	37.3351	1.30459
$820$	2.88027	0.100583
$821$	−7.01171	−0.244711	−0.122355	−	0.992486i	$-0.539045\pi$
$821$	−7.01171	−0.244711	−0.122355	+	0.992486i	$0.539045\pi$
$822$	−0.881452	−0.0307442
$823$	7.43798	0.259272	0.129636	−	0.991562i	$-0.458619\pi$
$823$	7.43798	0.259272	0.129636	+	0.991562i	$0.458619\pi$
$824$	−8.55165	−0.297911
$825$	−14.9391	−0.520112
$826$	11.6458	0.405208
$827$	−46.8003	−1.62741	−0.813703	−	0.581280i	$-0.802552\pi$
$827$	−46.8003	−1.62741	−0.813703	+	0.581280i	$0.802552\pi$
$828$	0	0
$829$	−9.21991	−0.320221	−0.160110	−	0.987099i	$-0.551185\pi$
$829$	−9.21991	−0.320221	−0.160110	+	0.987099i	$0.551185\pi$
$830$	−6.53083	−0.226689
$831$	−67.5711	−2.34402
$832$	−5.84087	−0.202496
$833$	−24.7514	−0.857585
$834$	7.19460	0.249129
$835$	−13.1008	−0.453372
$836$	33.5570	1.16059
$837$	17.4768	0.604088
$838$	−33.8546	−1.16949
$839$	−12.9459	−0.446942	−0.223471	−	0.974711i	$-0.571739\pi$
$839$	−12.9459	−0.446942	−0.223471	+	0.974711i	$0.571739\pi$
$840$	3.06146	0.105631
$841$	−15.8665	−0.547120
$842$	7.66275	0.264076
$843$	−58.4812	−2.01420
$844$	22.5279	0.775443
$845$	21.1158	0.726405
$846$	33.9697	1.16790
$847$	−12.7168	−0.436955
$848$	3.44915	0.118444
$849$	−63.8321	−2.19071
$850$	4.12307	0.141420
$851$	0	0
$852$	24.5647	0.841573
$853$	38.6286	1.32262	0.661309	−	0.750114i	$-0.270001\pi$
$853$	38.6286	1.32262	0.661309	+	0.750114i	$0.270001\pi$
$854$	0.432354	0.0147949
$855$	44.0955	1.50804
$856$	−7.43153	−0.254004
$857$	−5.80072	−0.198149	−0.0990744	−	0.995080i	$-0.531588\pi$
$857$	−5.80072	−0.198149	−0.0990744	+	0.995080i	$0.531588\pi$
$858$	87.2573	2.97891
$859$	−40.1255	−1.36906	−0.684532	−	0.728983i	$-0.739993\pi$
$859$	−40.1255	−1.36906	−0.684532	+	0.728983i	$0.739993\pi$
$860$	−7.83960	−0.267328
$861$	8.81784	0.300511
$862$	−18.7700	−0.639307
$863$	−23.5478	−0.801576	−0.400788	−	0.916171i	$-0.631264\pi$
$863$	−23.5478	−0.801576	−0.400788	+	0.916171i	$0.631264\pi$
$864$	−10.4318	−0.354898
$865$	2.74724	0.0934091
$866$	−29.6515	−1.00760
$867$	0.000876412 0	2.97645e−5 0
$868$	1.67270	0.0567753
$869$	75.5605	2.56321
$870$	−11.1123	−0.376742
$871$	−29.6248	−1.00380
$872$	3.35720	0.113689
$873$	6.30753	0.213478
$874$	0	0
$875$	−0.998427	−0.0337530
$876$	−33.3927	−1.12823
$877$	17.0123	0.574465	0.287233	−	0.957861i	$-0.407265\pi$
$877$	17.0123	0.574465	0.287233	+	0.957861i	$0.407265\pi$
$878$	−18.9319	−0.638922
$879$	−31.3845	−1.05857
$880$	4.87205	0.164237
$881$	−12.5437	−0.422607	−0.211303	−	0.977421i	$-0.567771\pi$
$881$	−12.5437	−0.422607	−0.211303	+	0.977421i	$0.567771\pi$
$882$	−38.4327	−1.29410
$883$	20.9605	0.705376	0.352688	−	0.935741i	$-0.385268\pi$
$883$	20.9605	0.705376	0.352688	+	0.935741i	$0.385268\pi$
$884$	−24.0823	−0.809977
$885$	35.7655	1.20224
$886$	19.5875	0.658055
$887$	−53.6485	−1.80134	−0.900670	−	0.434504i	$-0.856924\pi$
$887$	−53.6485	−1.80134	−0.900670	+	0.434504i	$0.856924\pi$
$888$	0.191398	0.00642290
$889$	−9.86685	−0.330923
$890$	6.54601	0.219423
$891$	62.2678	2.08605
$892$	−5.10636	−0.170974
$893$	36.5460	1.22297
$894$	−14.4188	−0.482238
$895$	4.68622	0.156643
$896$	−0.998427	−0.0333551
$897$	0	0
$898$	16.1589	0.539231
$899$	−6.07146	−0.202495
$900$	6.40210	0.213403
$901$	14.2211	0.473773
$902$	14.0328	0.467242
$903$	−24.0006	−0.798691
$904$	−9.89232	−0.329014
$905$	−21.3546	−0.709851
$906$	−38.4317	−1.27681
$907$	3.43065	0.113913	0.0569564	−	0.998377i	$-0.481860\pi$
$907$	3.43065	0.113913	0.0569564	+	0.998377i	$0.481860\pi$
$908$	15.7932	0.524116
$909$	111.214	3.68873
$910$	5.83169	0.193319
$911$	27.1854	0.900693	0.450346	−	0.892854i	$-0.351301\pi$
$911$	27.1854	0.900693	0.450346	+	0.892854i	$0.351301\pi$
$912$	−21.1195	−0.699338
$913$	−31.8185	−1.05304
$914$	35.7419	1.18224
$915$	1.32781	0.0438960
$916$	15.2178	0.502812
$917$	19.8893	0.656801
$918$	−43.0111	−1.41958
$919$	19.0098	0.627075	0.313537	−	0.949576i	$-0.398486\pi$
$919$	19.0098	0.627075	0.313537	+	0.949576i	$0.398486\pi$
$920$	0	0
$921$	68.4576	2.25575
$922$	−0.555235	−0.0182857
$923$	46.7926	1.54020
$924$	14.9156	0.490687
$925$	−0.0624202	−0.00205236
$926$	25.4438	0.836135
$927$	−54.7486	−1.79818
$928$	3.62402	0.118964
$929$	35.2838	1.15762	0.578812	−	0.815461i	$-0.303517\pi$
$929$	35.2838	1.15762	0.578812	+	0.815461i	$0.303517\pi$
$930$	5.13707	0.168451
$931$	−41.3476	−1.35511
$932$	22.1354	0.725068
$933$	68.2084	2.23304
$934$	−24.6453	−0.806418
$935$	20.0878	0.656941
$936$	−37.3939	−1.22226
$937$	12.7726	0.417263	0.208631	−	0.977994i	$-0.433099\pi$
$937$	12.7726	0.417263	0.208631	+	0.977994i	$0.433099\pi$
$938$	−5.06401	−0.165346
$939$	60.3012	1.96786
$940$	5.30601	0.173063
$941$	46.8978	1.52883	0.764413	−	0.644727i	$-0.223029\pi$
$941$	46.8978	1.52883	0.764413	+	0.644727i	$0.223029\pi$
$942$	−44.3663	−1.44553
$943$	0	0
$944$	−11.6641	−0.379634
$945$	10.4154	0.338814
$946$	−38.1949	−1.24182
$947$	37.8633	1.23039	0.615197	−	0.788374i	$-0.289077\pi$
$947$	37.8633	1.23039	0.615197	+	0.788374i	$0.289077\pi$
$948$	−47.5550	−1.54451
$949$	−63.6087	−2.06482
$950$	6.88766	0.223465
$951$	−26.5474	−0.860857
$952$	−4.11659	−0.133419
$953$	−15.5608	−0.504062	−0.252031	−	0.967719i	$-0.581099\pi$
$953$	−15.5608	−0.504062	−0.252031	+	0.967719i	$0.581099\pi$
$954$	22.0818	0.714925
$955$	−9.22931	−0.298653
$956$	10.1222	0.327375
$957$	−54.1395	−1.75008
$958$	−10.3284	−0.333695
$959$	−0.287014	−0.00926815
$960$	−3.06629	−0.0989639
$961$	−28.1932	−0.909459
$962$	0.364588	0.0117548
$963$	−47.5774	−1.53316
$964$	1.74704	0.0562685
$965$	8.47079	0.272685
$966$	0	0
$967$	1.27815	0.0411027	0.0205513	−	0.999789i	$-0.493458\pi$
$967$	1.27815	0.0411027	0.0205513	+	0.999789i	$0.493458\pi$
$968$	12.7368	0.409377
$969$	−87.0773	−2.79733
$970$	0.985227	0.0316337
$971$	−29.0123	−0.931049	−0.465524	−	0.885035i	$-0.654134\pi$
$971$	−29.0123	−0.931049	−0.465524	+	0.885035i	$0.654134\pi$
$972$	−7.89359	−0.253187
$973$	2.34267	0.0751025
$974$	−5.64762	−0.180961
$975$	17.9098	0.573572
$976$	−0.433035	−0.0138611
$977$	33.0235	1.05652	0.528258	−	0.849084i	$-0.322845\pi$
$977$	33.0235	1.05652	0.528258	+	0.849084i	$0.322845\pi$
$978$	5.83720	0.186653
$979$	31.8924	1.01929
$980$	−6.00314	−0.191763
$981$	21.4932	0.686224
$982$	8.94474	0.285438
$983$	49.4139	1.57606	0.788029	−	0.615638i	$-0.211102\pi$
$983$	49.4139	1.57606	0.788029	+	0.615638i	$0.211102\pi$
$984$	−8.83173	−0.281545
$985$	17.9878	0.573139
$986$	14.9421	0.475853
$987$	16.2442	0.517058
$988$	−40.2300	−1.27989
$989$	0	0
$990$	31.1913	0.991326
$991$	16.3157	0.518285	0.259143	−	0.965839i	$-0.416560\pi$
$991$	16.3157	0.518285	0.259143	+	0.965839i	$0.416560\pi$
$992$	−1.67534	−0.0531920
$993$	59.2232	1.87939
$994$	7.99863	0.253701
$995$	−0.823135	−0.0260951
$996$	20.0254	0.634529
$997$	−44.8057	−1.41901	−0.709505	−	0.704700i	$-0.751081\pi$
$997$	−44.8057	−1.41901	−0.709505	+	0.704700i	$0.751081\pi$
$998$	−23.1525	−0.732880
$999$	0.651157	0.0206017

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bl.1.2		15
23.15	odd	22		230.2.g.d.41.3	✓	30
23.20	odd	22		230.2.g.d.101.3	yes	30
23.22	odd	2		5290.2.a.bk.1.2		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.41.3	✓	30	23.15	odd	22
230.2.g.d.101.3	yes	30	23.20	odd	22
5290.2.a.bk.1.2		15	23.22	odd	2
5290.2.a.bl.1.2		15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.06629 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.06629 q^{6} -0.998427 q^{7} +1.00000 q^{8} +6.40210 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.06629 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.06629 q^{6} -0.998427 q^{7} +1.00000 q^{8} +6.40210 q^{9} +1.00000 q^{10} +4.87205 q^{11} -3.06629 q^{12} -5.84087 q^{13} -0.998427 q^{14} -3.06629 q^{15} +1.00000 q^{16} +4.12307 q^{17} +6.40210 q^{18} +6.88766 q^{19} +1.00000 q^{20} +3.06146 q^{21} +4.87205 q^{22} -3.06629 q^{24} +1.00000 q^{25} -5.84087 q^{26} -10.4318 q^{27} -0.998427 q^{28} +3.62402 q^{29} -3.06629 q^{30} -1.67534 q^{31} +1.00000 q^{32} -14.9391 q^{33} +4.12307 q^{34} -0.998427 q^{35} +6.40210 q^{36} -0.0624202 q^{37} +6.88766 q^{38} +17.9098 q^{39} +1.00000 q^{40} +2.88027 q^{41} +3.06146 q^{42} -7.83960 q^{43} +4.87205 q^{44} +6.40210 q^{45} +5.30601 q^{47} -3.06629 q^{48} -6.00314 q^{49} +1.00000 q^{50} -12.6425 q^{51} -5.84087 q^{52} +3.44915 q^{53} -10.4318 q^{54} +4.87205 q^{55} -0.998427 q^{56} -21.1195 q^{57} +3.62402 q^{58} -11.6641 q^{59} -3.06629 q^{60} -0.433035 q^{61} -1.67534 q^{62} -6.39204 q^{63} +1.00000 q^{64} -5.84087 q^{65} -14.9391 q^{66} +5.07198 q^{67} +4.12307 q^{68} -0.998427 q^{70} -8.01123 q^{71} +6.40210 q^{72} +10.8903 q^{73} -0.0624202 q^{74} -3.06629 q^{75} +6.88766 q^{76} -4.86438 q^{77} +17.9098 q^{78} +15.5090 q^{79} +1.00000 q^{80} +12.7806 q^{81} +2.88027 q^{82} -6.53083 q^{83} +3.06146 q^{84} +4.12307 q^{85} -7.83960 q^{86} -11.1123 q^{87} +4.87205 q^{88} +6.54601 q^{89} +6.40210 q^{90} +5.83169 q^{91} +5.13707 q^{93} +5.30601 q^{94} +6.88766 q^{95} -3.06629 q^{96} +0.985227 q^{97} -6.00314 q^{98} +31.1913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} + 15 q^{5} + 5 q^{6} - 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 + 15 * q^5 + 5 * q^6 - 4 * q^7 + 15 * q^8 + 28 * q^9	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} + 15 q^{5} + 5 q^{6} - 4 q^{7} + 15 q^{8} + 28 q^{9} + 15 q^{10} + 7 q^{11} + 5 q^{12} + 17 q^{13} - 4 q^{14} + 5 q^{15} + 15 q^{16} + 2 q^{17} + 28 q^{18} + 18 q^{19} + 15 q^{20} + 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} - 4 q^{28} + 35 q^{29} + 5 q^{30} + 19 q^{31} + 15 q^{32} - 21 q^{33} + 2 q^{34} - 4 q^{35} + 28 q^{36} - 12 q^{37} + 18 q^{38} + 26 q^{39} + 15 q^{40} + 27 q^{41} + 12 q^{43} + 7 q^{44} + 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} - 27 q^{51} + 17 q^{52} - 20 q^{53} + 29 q^{54} + 7 q^{55} - 4 q^{56} - 11 q^{57} + 35 q^{58} + 15 q^{59} + 5 q^{60} + 28 q^{61} + 19 q^{62} - 51 q^{63} + 15 q^{64} + 17 q^{65} - 21 q^{66} + 4 q^{67} + 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} - 12 q^{74} + 5 q^{75} + 18 q^{76} + 45 q^{77} + 26 q^{78} - 2 q^{79} + 15 q^{80} + 79 q^{81} + 27 q^{82} - 29 q^{83} + 2 q^{85} + 12 q^{86} - 7 q^{87} + 7 q^{88} + 20 q^{89} + 28 q^{90} + 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} - 22 q^{97} + 29 q^{98} + 23 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 + 15 * q^5 + 5 * q^6 - 4 * q^7 + 15 * q^8 + 28 * q^9 + 15 * q^10 + 7 * q^11 + 5 * q^12 + 17 * q^13 - 4 * q^14 + 5 * q^15 + 15 * q^16 + 2 * q^17 + 28 * q^18 + 18 * q^19 + 15 * q^20 + 7 * q^22 + 5 * q^24 + 15 * q^25 + 17 * q^26 + 29 * q^27 - 4 * q^28 + 35 * q^29 + 5 * q^30 + 19 * q^31 + 15 * q^32 - 21 * q^33 + 2 * q^34 - 4 * q^35 + 28 * q^36 - 12 * q^37 + 18 * q^38 + 26 * q^39 + 15 * q^40 + 27 * q^41 + 12 * q^43 + 7 * q^44 + 28 * q^45 + 40 * q^47 + 5 * q^48 + 29 * q^49 + 15 * q^50 - 27 * q^51 + 17 * q^52 - 20 * q^53 + 29 * q^54 + 7 * q^55 - 4 * q^56 - 11 * q^57 + 35 * q^58 + 15 * q^59 + 5 * q^60 + 28 * q^61 + 19 * q^62 - 51 * q^63 + 15 * q^64 + 17 * q^65 - 21 * q^66 + 4 * q^67 + 2 * q^68 - 4 * q^70 + 22 * q^71 + 28 * q^72 + 48 * q^73 - 12 * q^74 + 5 * q^75 + 18 * q^76 + 45 * q^77 + 26 * q^78 - 2 * q^79 + 15 * q^80 + 79 * q^81 + 27 * q^82 - 29 * q^83 + 2 * q^85 + 12 * q^86 - 7 * q^87 + 7 * q^88 + 20 * q^89 + 28 * q^90 + 6 * q^91 + 63 * q^93 + 40 * q^94 + 18 * q^95 + 5 * q^96 - 22 * q^97 + 29 * q^98 + 23 * q^99

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